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Geometry and Dynamical Systems in Machine Learning and Control


Dorobantu, Victor David (2023) Geometry and Dynamical Systems in Machine Learning and Control. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/x271-r088.


For many problems of interest in machine learning and control, we have access to rich information about underlying geometry and dynamics; we can leverage this information to build robust and performant solutions in new algorithms, optimizations, and designs. In this thesis we study four problem settings to stress this central assumption. First, we study conformal generative modeling, using computational geometry techniques to simplify and register complex 2D surfaces and enabling the use of a variety of flow-based generative models as plug-and-play subroutines. Second, we study data-driven robust optimization problems in control, modeling the precise impact of dynamics uncertainty in several control frameworks using convex geometry. Third, we study compactly-restrictable policy optimization, constraining the available states and actions in reinforcement learning and optimal control problems to be consistent with the inherent dynamics of the systems to be controlled. Finally, we study nonlinear model predictive control on Lie groups as applied to a 3D hopping robot platform, developing a control methodology compatible with nontrivial state space geometry and hybrid system dynamics.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Geometry; Dynamical Systems; Machine Learning; Control; Generative Modeling; Continuous Normalizing Flows; Moser Flows; Conformal Geometry; Convex Optimization; Robust Optimization; Control-Affine Systems; Convex Geometry; Optimal Control; Reinforcement Learning; Value Iteration; Lie Groups; Robotics; Model Predictive Control; Hybrid Systems; Lie Group Integrators; Sampled-Data Control; Stability; Safety
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Computing and Mathematical Sciences
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Yue, Yisong
Thesis Committee:
  • Dabiri, John O. (chair)
  • Schroeder, Peter
  • Azizzadenesheli, Kamyar
  • Yue, Yisong
Defense Date:25 May 2023
Funding AgencyGrant Number
Department of Energy (DOE)DE-AC52-07NA27344
Department of Energy (DOE)EC-SRP-21-0101
Record Number:CaltechTHESIS:06012023-194820518
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for Chapter 2 adapted for Chapter 3 adapted for Chapter 4 adapted for Chapter 5 adapted for Appendix adapted for Appendix
Dorobantu, Victor David0000-0002-2797-7802
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15260
Deposited By: Victor Dorobantu
Deposited On:02 Jun 2023 15:47
Last Modified:09 Jun 2023 18:53

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